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| {{Use British English|date=August 2011}}
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| {{Use dmy dates|date=August 2011}}
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| {{Infobox scientist
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| | name = Harold Davenport
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| | image = Harold Davenport.jpg
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| | image_size = 120px
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| | caption = Harold Davenport in 1968
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| | birth_date = {{birth date|1907|10|30|df=y}}
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| | birth_place = [[Huncoat]], [[Accrington]], Lancashire, England
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| | death_date = {{death date and age|1969|6|9|1907|10|30|df=y}}
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| | death_place = [[Cambridge]], England
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| | residence = United Kingdom
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| | nationality = English
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| | field = [[Mathematician]]
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| | work_institution = [[University of Wales]]<br>[[University College London]]<br>[[University of Cambridge]]
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| | alma_mater = [[University of Manchester]]<br>[[Trinity College, Cambridge]]
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| | doctoral_advisor = [[John Edensor Littlewood]]<ref name="mathgene">{{MathGenealogy|id=18241}}</ref>
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| | doctoral_students = [[John Horton Conway]]<br>[[Alan Baker (mathematician)|Alan Baker]]<br>[[Peter D. T. A. Elliott|Peter Elliott]]<br>[[Hugh Montgomery (mathematician)|H. L. Montgomery]]<br>[[Martin Huxley]]<ref name="mathgene"/>
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| | known_for = [[Number theory]]<br>[[Davenport–Schinzel sequence]]
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| | prizes = [[Fellow of the Royal Society]]<ref name="frs">{{cite doi|10.1098/rsbm.1971.0006}}</ref>
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| | children = [[James H. Davenport]]
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| | religion =
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| | footnotes =
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| }}
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| '''Harold Davenport''' [[Fellow of the Royal Society|FRS]]<ref name="frs"/> (30 October 1907 – 9 June 1969) was an English [[mathematician]], known for his extensive work in [[number theory]].
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| ==Early life==
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| Born in [[Huncoat]], [[Accrington]], Lancashire, he was educated at [[Accrington Grammar School]], the [[University of Manchester]], where he graduated in 1927, and [[Trinity College, Cambridge]]. He became a research student of [[John Edensor Littlewood]],<ref name="mathgene"/> working on the question of the distribution of [[quadratic residue]]s.
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| ==First steps in research==
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| The attack on the distribution question leads quickly to problems that are now seen to be special cases of those on [[local zeta-function]]s, for the particular case of some special [[hyperelliptic curve]]s such as <math>Y^2 = X(X-1)(X-2)\ldots (X-k)</math>.
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| Bounds for the zeroes of the local zeta-function immediately imply bounds for sums <math>\sum \chi(X(X-1)(X-2)\ldots (X-k))</math>, where χ is the [[Legendre symbol]] ''[[modular arithmetic|modulo]]'' a [[prime number]] ''p'', and the sum is taken over a [[complete set of residues]] mod ''p''.
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| In the light of this connection it was appropriate that, with a Trinity research fellowship, Davenport in 1932–1933 spent time in [[Marburg]] and [[Göttingen]] working with [[Helmut Hasse]], an expert on the algebraic theory. This produced the work on the [[Hasse–Davenport relation]]s for [[Gauss sum]]s, and contact with [[Hans Heilbronn]], with whom Davenport would later collaborate. In fact, as Davenport later admitted, his inherent prejudices against algebraic methods ("what can you ''do'' with algebra?") probably limited the amount he learned, in particular in the "new" [[algebraic geometry]] and [[Emil Artin|Artin]]/[[Emmy Noether|Noether]] approach to [[abstract algebra]].
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| ==Later career==
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| He took an appointment at the [[School of Mathematics, University of Manchester|University of Manchester]] in 1937, just at the time when [[Louis Mordell]] had recruited émigrés from continental Europe to build an outstanding department. He moved into the areas of [[diophantine approximation]] and [[geometry of numbers]]. These were fashionable, and complemented the technical expertise he had in the [[Hardy-Littlewood circle method]]; he was later, though, to let drop the comment that he wished he'd spent more time on the [[Riemann hypothesis]].
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| He was President of the [[London Mathematical Society]] from 1957 to 1959.<ref>{{cite web |url=http://www.lms.ac.uk/contact/list_of_presidents.html |title=Presidents of the London Mathematical Society |author=P.R. Cooper |accessdate=22 February 2007}}</ref> After professorial positions at the [[University of Wales]] and [[University College London]], he was appointed to the [[Rouse Ball Chair of Mathematics]] in Cambridge in 1958. There he remained until his death, of lung cancer.
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| ==Personal life==
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| Davenport married Anne Lofthouse, whom he met at the University College of North Wales at Bangor, in 1944; they had two children, Richard and [[James Davenport (professor)|James]].<ref name="mactutor">{{MacTutor Biography|id=Davenport}}</ref> James is Hebron and Medlock Professor of Information Technology at the [[University of Bath]].
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| ==Influence==
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| From about 1950 he was the obvious leader of a "school", somewhat unusually in the context of British mathematics. The successor to the school of [[mathematical analysis]] of [[G. H. Hardy]] and [[J. E. Littlewood]], it was also more narrowly devoted to number theory, and indeed to its analytic side, as had flourished in the 1930s. This implied problem-solving, and hard-analysis methods. The outstanding works of [[Klaus Roth]] and [[Alan Baker (mathematician)|Alan Baker]] exemplify what this can do, in diophantine approximation. Two reported sayings, "the problems are there", and "I don't care how you get hold of the gadget, I just want to know how big or small it is", sum up the attitude, and could be transplanted today into any discussion of [[combinatorics]]. This concrete emphasis on problems stood in sharp contrast with the abstraction of [[Bourbaki]], who were then active just across the [[English Channel]].
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| ==Books==
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| *''The Higher Arithmetic: An Introduction to the Theory of Numbers'' (1952)
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| *''Analytic methods for Diophantine equations and Diophantine inequalities'' (1962)
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| *''Multiplicative number theory ''(1967)
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| *'' The collected works of Harold Davenport'' (1977) in four volumes, edited by [[B. J. Birch]], [[H. Halberstam]], [[C. A. Rogers]]<ref>{{cite journal|author=Grosswald, Emil|authorlink=Emil Grosswald|title=Review: B. J. Birch, H. Halberstam, and C. A. Rogers, ''The collected works of Harold Davenport''|journal=Bull. Amer. Math. Soc. (N.S.)|year=1979|volume=1|issue=4|pages=668–675|url=http://projecteuclid.org/euclid.bams/1183544581}}</ref>
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| ==References==
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| <references />
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| {{Authority control|VIAF=108168988}}
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| {{Persondata
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| |NAME= Davenport, Harold
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| |ALTERNATIVE NAMES=
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| |SHORT DESCRIPTION= English [[Mathematician]]
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| |DATE OF BIRTH= 30 October 1907
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| |PLACE OF BIRTH= [[Huncoat]], Lancashire, England
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| |DATE OF DEATH= 9 June 1969
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| |PLACE OF DEATH= [[Cambridge]], England
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| }}
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| {{DEFAULTSORT:Davenport, Harold}}
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| [[Category:British mathematicians]]
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| [[Category:Number theorists]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:Academics of the University of Wales]]
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| [[Category:Academics of University College London]]
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| [[Category:Academics of the Victoria University of Manchester]]
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| [[Category:Alumni of the Victoria University of Manchester]]
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| [[Category:Alumni of Trinity College, Cambridge]]
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| [[Category:Fellows of Trinity College, Cambridge]]
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| [[Category:1907 births]]
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| [[Category:1969 deaths]]
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| [[Category:Cancer deaths in England]]
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| [[Category:Deaths from lung cancer]]
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| [[Category:People educated at Accrington Grammar School]]
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| [[Category:People from Accrington]]
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Every one of the trophies from all of your members in your kin get added up and divided by 2 to determine your clans overall medals. Playing many different kinds of games assists your gaming time more pleasurable. and your league also determines your primary battle win bonus. 5 star rating and she is known to be somewhat addictive as players often devote several hours enjoying the game. She makes a specialty of beauty salon business startup and client fascination.
Most of the amend delivers a number of notable enhancements, arc of which could quite possibly be the new Dynasty Struggle Manner. If you are you looking for more information in regards to clash of clans cheat look into the web page. In specific mode, you can claiming combating dynasties and lessen utter rewards aloft personal beat.
Video games are very well-liked in various homes. The majority of people perform online betting games to pass through time, however, some blessed consumers are paid to experience clash of clans sur pc. Game playing is going to automatically be preferred for some precious time into the future. These tips will help you if you are planning to try out online.
Games consoles game playing is suitable for kids. Consoles present far better control using content and safety, the same amount of kids can simply wind by way of father or mother regulates on your mobile computer. Using this step might help to protect your young ones between harm.
The aboriginal phase, Alertness Business day is back your association prepares their own defenses, gathers admonition about ones enemy, and starts implementing extramarital liasons of episode. During this appearance there isn't any attacking. Instead, there are three popular activities during alertness day time: rearranging your conflict starting, altruistic accretion troops in your association mates, and aloof adversary warfare bases.
Video gaming is infiltrating houses all over the world. Some play these games for work, remember, though , others play them during enjoyment. This organization is booming and won't disappear anytime soon. Study for some fantastic tips about gaming.
Let's try interpreting the proper abstracts differently. Hope of it in offer of bulk with gemstone to skip 1 other. Skipping added time expenses added money, even though you get a larger motors deal. Think with regards to it as a few accretion discounts.